Best Known (79, 109, s)-Nets in Base 9
(79, 109, 760)-Net over F9 — Constructive and digital
Digital (79, 109, 760)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (2, 17, 20)-net over F9, using
- net from sequence [i] based on digital (2, 19)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 2 and N(F) ≥ 20, using
- net from sequence [i] based on digital (2, 19)-sequence over F9, using
- digital (62, 92, 740)-net over F9, using
- trace code for nets [i] based on digital (16, 46, 370)-net over F81, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 16 and N(F) ≥ 370, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
- trace code for nets [i] based on digital (16, 46, 370)-net over F81, using
- digital (2, 17, 20)-net over F9, using
(79, 109, 6577)-Net over F9 — Digital
Digital (79, 109, 6577)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(9109, 6577, F9, 30) (dual of [6577, 6468, 31]-code), using
- construction X applied to Ce(29) ⊂ Ce(25) [i] based on
- linear OA(9105, 6561, F9, 30) (dual of [6561, 6456, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 6560 = 94−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(993, 6561, F9, 26) (dual of [6561, 6468, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 6560 = 94−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(94, 16, F9, 3) (dual of [16, 12, 4]-code or 16-cap in PG(3,9)), using
- construction X applied to Ce(29) ⊂ Ce(25) [i] based on
(79, 109, 6899829)-Net in Base 9 — Upper bound on s
There is no (79, 109, 6899830)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 102 904515 433372 943224 080776 147748 103069 648988 369146 665951 781275 654993 755651 473180 077479 070491 515522 970769 > 9109 [i]